anonymous
  • anonymous
A food store makes a 11–pound mixture of peanuts, almonds, and raisins. The cost of peanuts is $1.50 per pound, almonds cost $3.00 per pound, and raisins cost $1.50 per pound. The mixture calls for twice as many peanuts as almonds. The total cost of the mixture is $21.00. How much of each ingredient did the store use? 3 lbs peanuts, 6 lbs almonds, 2 lbs raisins 8 lbs peanuts, 1 lb almonds, 2 lbs raisins 6 lbs peanuts, 3 lbs almonds, 2 lbs raisins 8 lbs peanuts, 2 lbs almonds, 1 lbs raisins
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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jamiebookeater
  • jamiebookeater
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jim_thompson5910
  • jim_thompson5910
Start off by defining variables
jim_thompson5910
  • jim_thompson5910
let x = amount of peanuts (in pounds), y = amount of almonds (in pounds) and z = amount of raisins (in pounds)
anonymous
  • anonymous
okey (:

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jim_thompson5910
  • jim_thompson5910
If "A food store makes a 11–pound mixture of peanuts, almonds, and raisins" then what does this mean?
anonymous
  • anonymous
That they add up to 11 pounds haha
jim_thompson5910
  • jim_thompson5910
good, so x y and z add to 11, which means x+y+z = 11
jim_thompson5910
  • jim_thompson5910
that's one equation
anonymous
  • anonymous
so x+y+z=11 :o
jim_thompson5910
  • jim_thompson5910
yes
anonymous
  • anonymous
But then we have to factor in how much they cost..
jim_thompson5910
  • jim_thompson5910
We also know that "The cost of peanuts is $1.50 per pound, almonds cost $3.00 per pound, and raisins cost $1.50 per pound" So x lbs of peanuts cost 1.5x dollars, y lbs of almonds cost 3y dollars, and z lbs of raisins cost 1.5z dollars They total 1.5x + 3y + 1.5z dollars
jim_thompson5910
  • jim_thompson5910
this total cost is given to be $21 so 1.5x + 3y + 1.5z = 21
anonymous
  • anonymous
so like, 1.50x+3.00y+1.50=21..
anonymous
  • anonymous
Haha Okey you already said that x.x my bad
anonymous
  • anonymous
1.50z* I meant btw haha. I get that indeed.
jim_thompson5910
  • jim_thompson5910
close, you mean to say 1.50x+3.00y+1.50z=21 but you got it
anonymous
  • anonymous
And don't forget twice the peanuts!
jim_thompson5910
  • jim_thompson5910
that's your 2nd equation
jim_thompson5910
  • jim_thompson5910
twice the peanuts as what?
anonymous
  • anonymous
it says, the recipe calls for twice as many peanuts as almonds O.o
jim_thompson5910
  • jim_thompson5910
good, so the equation for that is?
anonymous
  • anonymous
ermm.. I dunno lol.. x(times2y)+y+z=11 O.O I have no idea.
jim_thompson5910
  • jim_thompson5910
not quite
anonymous
  • anonymous
knew it was wrong x.x
jim_thompson5910
  • jim_thompson5910
Amount of peanuts = 2 times (amount of almonds)
jim_thompson5910
  • jim_thompson5910
y = 2 times x or just y = 2x
anonymous
  • anonymous
oh pshh I should have thought of that x.x
jim_thompson5910
  • jim_thompson5910
so you have these 3 equations x+y+z = 11 1.5x + 3y + 1.5z = 21 y = 2x
jim_thompson5910
  • jim_thompson5910
you can use them to solve for x, y and z
jim_thompson5910
  • jim_thompson5910
I'll get you started
anonymous
  • anonymous
Lol I can't because I'm stupid, But smart people definitely can haha
jim_thompson5910
  • jim_thompson5910
x+y+z = 11 x+2x+z = 11 3x+z = 11 --------------------- 1.5x + 3y + 1.5z = 21 1.5x + 3(2x) + 1.5z = 21 1.5x + 6x + 1.5z = 21 7.5x + 1.5z = 21
jim_thompson5910
  • jim_thompson5910
so after plugging in y = 2x, you now have the new system 3x+z = 11 7.5x + 1.5z = 21
anonymous
  • anonymous
O.o That all made absolutely no sense to me but it seems to for you and that's good enough for me
jim_thompson5910
  • jim_thompson5910
where are you lost?
jim_thompson5910
  • jim_thompson5910
I took x+y+z = 11 plugged in y = 2x (ie replaced every 'y' with '2x') to get x+2x+z = 11 then I combined like terms to get 3x+z = 11
jim_thompson5910
  • jim_thompson5910
I did the same with 1.5x + 3y + 1.5z = 21 to get 7.5x + 1.5z = 21
anonymous
  • anonymous
oh okay ! I see now, sorry it's really late and I'm super tired :/
jim_thompson5910
  • jim_thompson5910
so you have 3x+z = 11 7.5x + 1.5z = 21 now
jim_thompson5910
  • jim_thompson5910
solve the first equation for z to get this 3x+z = 11 3x+z - 3x = 11 - 3x z = 11 - 3x
anonymous
  • anonymous
Alrighty
jim_thompson5910
  • jim_thompson5910
Since z = 11 - 3x, you can plug it into the other equation and solve for x 7.5x + 1.5z = 21 7.5x + 1.5(11 - 3x) = 21 Solve for x
jim_thompson5910
  • jim_thompson5910
oh wait, i made a variable mistake...i switched x and y one sec
jim_thompson5910
  • jim_thompson5910
Let me fix real quick
anonymous
  • anonymous
I was thinking that haha x) ..
anonymous
  • anonymous
uhh ? your comment disappeared .. :o
jim_thompson5910
  • jim_thompson5910
it should be x = 2y, not y = 2x so x+y+z = 11 2y+y+z = 11 3y + z = 11 z = 11 - 3y --------------------------- 1.5x + 3y + 1.5z = 21 1.5(2y) + 3y + 1.5z = 21 3y + 3y + 1.5z = 21 6y + 1.5z = 21 =========================== 6y + 1.5z = 21 6y + 1.5(11 - 3y) = 21 Solve that last equation for y
jim_thompson5910
  • jim_thompson5910
sry
jim_thompson5910
  • jim_thompson5910
Solve 6y + 1.5(11 - 3y) = 21 for y
anonymous
  • anonymous
haha it's okay
anonymous
  • anonymous
Aw man I have to go to bed soon I'm dead tired x.x
jim_thompson5910
  • jim_thompson5910
What do you get when you solve that equation for y
anonymous
  • anonymous
ergh I dunno x.x I'm brain dead
jim_thompson5910
  • jim_thompson5910
Then give it a break, get some sleep and you'll tackle it in the morning
anonymous
  • anonymous
Oh no I keep losing connection >.<

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